% Mizar problem: e4_79_1_1,cgames_1,2037,26 
include('Axioms/SET010^0.ax').
thf(c1_79_1_1_type,type,( c1_79_1_1__cgames_1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k8_cgames_1_type,type,( k8_cgames_1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_cgames_1_type,type,( v2_cgames_1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k8_cgames_1,axiom,( $true ),file(cgames_1,k8_cgames_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_79_1_1__cgames_1,axiom,( ( v1_relat_1 @ c1_79_1_1__cgames_1 ) & ( v1_funct_1 @ c1_79_1_1__cgames_1 ) ),file(cgames_1,c1_79_1_1__cgames_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc4_cgames_1,axiom,( ? [A: $i] : ( v2_cgames_1 @ A ) ),file(cgames_1,rc4_cgames_1)).
thf(e3_79_1_1__cgames_1,axiom,( ! [A: $i] : ( ( v2_cgames_1 @ A ) => ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( ( r2_hidden @ B @ ( k8_cgames_1 @ A ) ) => ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_79_1_1__cgames_1 ) ) => ( v2_cgames_1 @ ( k1_funct_1 @ c1_79_1_1__cgames_1 @ B ) ) ) ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_79_1_1__cgames_1 ) ) => ( v2_cgames_1 @ ( k1_funct_1 @ c1_79_1_1__cgames_1 @ A ) ) ) ) ) ),file(cgames_1,e3_79_1_1__cgames_1)).
thf(s3_cgames_1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( ! [C: $i] : ( ( v2_cgames_1 @ C ) => ( ( r2_hidden @ C @ ( k8_cgames_1 @ B ) ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( A @ B ) ) ) ),file(cgames_1,s3_cgames_1)).
thf(e4_79_1_1__cgames_1,conjecture,( ! [A: $i] : ( ( v2_cgames_1 @ A ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_79_1_1__cgames_1 ) ) => ( v2_cgames_1 @ ( k1_funct_1 @ c1_79_1_1__cgames_1 @ A ) ) ) ) ),file(cgames_1,e4_79_1_1__cgames_1)).
